Bead models are used in dynamical simulation of tethers. These models discretize a cable using beads distributed along its length. The time evolution is obtained numerically. Typically the number of particles ranges between 5 and 50, depending on the required accuracy. Sometimes the simulation is extended over long periods (several years). The complex interactions between the cable and its spatial environment require to optimize the propagators -both in runtime and precisionthat constitute the central core of the process. The special perturbation method treated on this article conjugates simpleness of computer implementation, speediness and precision, and is capable to propagate the orbit of whichever material particle. The paper describes the evolution of some orbital elements, which are constants in a non-perturbed problem, but which evolve in the time scale imposed by the perturbation. It can be used with any kind of orbit and it is free of singularities related to small inclination and/or small eccentricity. The use of Euler parameters makes it robust.

The computation of the Minimum Orbital Intersection Distance (MOID) is an old, but increasingly relevant problem. Fast and precise methods for MOID computation are needed to select potentially hazardous asteroids from a large catalogue. The same applies to debris with respect to spacecraft. An iterative method that strictly meets these two premises is presented.

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emergency landings, aborted take-offs etc. A meaningful fraction of fatalities occurring in these situations is related to fire and toxic environments. Therefore, a key factor for survival is the ability to quickly evacuate the aeroplane (1-3) . To improve passenger and crew safety in such circumstances, airworthiness authorities require manufacturers and operators to meet a number of design and performance standards related to cabin evacuation (4,5) . One of these regulations, albeit quite controversial, is the 90-second rule which requires the demonstration in any new or derivative-type aeroplane that all occupants can safely abandon the aircraft in less than 90s, with half of the usable exits blocked, minimum illumination provided by floor proximity lighting, and a certain age-gender mix in the simulated occupants.The rule was established in 1965 with 120 seconds, and has been evolving over the years to encompass the improvements in escape equipment (3,6) , changes in cabin and seat material (2,7) and more complete and appropriate crew training (1,(8)(9)(10)(11) . A recent amendment to FAR regulations (4) has introduced new exit types and new conditions to perform or assess evacuation demonstrations; although some questions are still open. Table 1 summarises the updated exit types, including the new type B and C categories.The unique objective of the demonstration is to show that the aeroplane can be evacuated in less than 90s under the aforementioned conditions. It does not represent accident scenarios nor is intended for system optimisation. The demonstration only provides an industrial benchmark for consistent evaluation. However, the information provided on the random variable 'evacuation time' by a ABSTRACTThe present paper describes a new, agent-based computer model that can simulate the evacuation of narrow body transport aeroplanes in the conditions prescribed by the airworthiness regulations for certification. The input data are extracted from a complete plan view of the cabin. The results include full egress details of all occupants, passengers and crew-members, and the most significant evacuation figures and diagrams. The model has been tuned and verified with real data of narrow body certification demonstrations. Numerical simulations of six narrow body aircraft, representative of current designs, show the capabilities of the model and provide relevant information on the relationship between cabin features and emergency evacuation results. Although the computer model has been developed for helping in the certification process it would be useful too in the design of new cabins.

This paper presents the results obtained with a new agent-based computer model that can simulate the evacuation of narrow-body transport airplanes in the conditions prescribed by the airworthiness regulations for certification. The model, described in detail in a former paper, has been verified with real data of narrow-body certification demonstrations. Numerical simulations of around 20 narrow-body aircraft, representative of current designs in various market segments, show the capabilities of the model and provide relevant information on the relationship between cabin features and emergency evacuation. The longitudinal location of emergency exits seems to be even more important than their size or the overall margin with respect to the prescribed number and type of exits indicated by the airworthiness requirements.Nomenclature ETR = evacuation time ratio, T eva =90 N att = number of cabin attendants N flg = number of flight crew members N max = maximum number of seats according to number and type of exits in cabin N pax = number of passengers onboard N seat = number of seats in cabin Oxyz = reference system to locate all elements of cabin SCR = seating capacity ratio, N seat =N max T eva = evacuation time, t end t sta , s; also average evacuation time in a series of simulation runs T 95 = 95% confidence interval of evacuation time t end = time point when last occupant reaches ground or safe place t fee = time point when first exit is unoccupied t lea = time point when last exit is operative t sta = time origin of simulation run eva = standard deviation of evacuation time in series of simulation runs, s

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The minimum orbital intersection distance is used as a measure to assess potential close approaches and collision risks between astronomical objects. Methods to calculate this quantity have been proposed in several previous publications. The most frequent case is that in which both objects have elliptical osculating orbits. When at least one of the two orbits has low eccentricity, the latter can be used as a small parameter in an asymptotic power series expansion. The resulting approximation can be exploited to speed up the computation with negligible cost in terms of accuracy. This contribution introduces two asymptotic procedures into the SDG-MOID method presented in a previous article, it discusses the results of performance tests and their comparisons with previous findings. The best approximate procedure yields a reduction of 40% in computing speed without degrading the accuracy of the determinations. This remarkable result suggests that large benefits can be obtained in applications involving massive distance computations, such as in the analysis of large databases, in Monte Carlo simulations for impact risk assessment or in the long-time monitoring of the MOID between two objects.